Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times-Reference-Cited by-同舟云学术

Large Fork-Join Queues with Nearly Deterministic Arrival and Service Times

Published:2021-12-14 Issue: Volume: Page:
ISSN:0364-765X
Container-title:Mathematics of Operations Research
language:en
Short-container-title:Mathematics of OR

Author:

Schol Dennis¹^ORCID,Vlasiou Maria¹²^ORCID,Zwart Bert¹³^ORCID

Affiliation:

1. Eindhoven University of Technology, 5600 MB Eindhoven, Netherlands;

2. University of Twente, 7522 NB Enschede, Netherlands;

3. Centrum Wiskunde & Informatica, 1098 XG Amsterdam, Netherlands

Abstract

In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as [Formula: see text]. This fluid limit depends on the initial number of tasks. In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Management Science and Operations Research,Computer Science Applications,General Mathematics

Reference20 articles.

1. Maxima of Poisson-like variables and related triangular arrays

2. Queueing models for systems with synchronization constraints

3. Extreme values of independent stochastic processes

4. Almost sure limit sets of random samples in ℝd

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